I imagine there's some sort of storage system, like a huge bank of ultra-capacitors, that are constantly kept charged.
The wind up would be if that bank is depleted and they need to recharge. Delivering 100kW for a short period of time is definitely a feat.
Ah, good point, that seems likely.
If these things are even 50% efficient, then power delivery is really not a problem these days. Most EVs have no problem delivering 200kW for quite a few seconds at a time, limited mostly by components getting warm. Higher-end EVs are generally rated for 300-500kW.
It would by amusing to see one of these lasers mounted on an EV, possibly with a small range extender to recharge it on the go.